A circular metal shaft is being used to transmit power. It is known that at a certain critical angular velocity ω, any jarring of the shaft during rotation will cause the shaft to deform or buckle. This is a dangerous situation because the shaft might shatter under the increased centrifugal force. To find this critical velocity ω, we must first compute a number x that satisfies the equation
tan x + tanh x = 0
This number is then used in a formula to obtain ω. Solve for x (x > 0).
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